Mixed $H_2/H_\infty$ Fuzzy Control Plus Mobile Actuator/Sensor Guidance for Semilinear Parabolic Distributed Parameter Systems

Abstract

This article addresses the issue of fuzzy control design subject to a mixed $H_2/H_\infty$ performance constraint and guidance law design for semilinear parabolic distributed parameter systems (DPSs) with mobile collocated actuator/sensor pairs. Initially, via the local sector nonlinearity method, a Takagi–Sugeno (T–S) fuzzy model is constructed to accurately describe the spatiotemporal dynamics of the DPSs. Then, based on the obtained T–S fuzzy model and Lyapunov technique, a membership-function-dependent mixed $H_2/H_\infty$ fuzzy control design is developed and the mobile actuator/sensor guidance laws are also determined simultaneously, such that the resulting closed-loop system is exponentially stable while providing an $H_2$ performance bound under the given $H_\infty$ performance of disturbance attenuation, and the transient response of closed-loop state is improved. Moreover, a suboptimal mixed $H_2/H_\infty$ fuzzy control design is derived in the sense of minimizing the upper bound of the given $H_2$ performance function by applying the existing linear matrix inequality optimization techniques. At last, some simulation results for a numerical example are presented to verify the proposed method.